Influence of mesh-dependent Korn's inequality on the convergence of nonconforming finite element schemes

Abstrakt

We discuss the validity of a discrete analogue of Korn's first inequality for two-dimensional nonconforming finite elements. For the Crouzeix-Raviart element and the rotated bilinear element, the constant in this inequality is mesh-dependent and we investigate its influence on the convergence properties of finite element discretizations of the Stokes equations involving deformation tensor formulation of the Laplace operator.

Whereas for the rotated bilinear element convergence results can be proved, no convergence of the standard discretization can be expected if the Crouzeix-Raviart element is applied.